Project presentations¶
Present a biology/medicine themed paper that incorporates 'substantial' python implementation.¶
Dates: December 5 and December 10¶
Papers can be from diverse areas of computational biology and medicine including but not limited to: systems biology, bioinformatics, computational structural biology, computational medicine, bioimaging, etc.
Details
- You can work in groups of no more than 3 people.
- All three group members will be required to present.
- The presentation should be 12 mins + 3 mins questions.
- The presentation should include:
- What the paper is about.
- A clear description of the python based coding done in the paper (including any packages you found interesting).
- How that work helped the authors achieve the results they presented in the paper
OMET Teaching Survey¶
Please fill out.
Networks¶
Terminology alert: networks of neurons are sometimes called multilayer perceptrons, despite not using the step function.
Neural Networks¶
The universal approximation theorem says that, if some reasonable assumptions are made, a feedforward neural network with a finite number of nodes can approximate any continuous function to within a given error $\epsilon$ over a bounded input domain.
The theorem says nothing about the design (number of nodes/layers) of such a network.
The theorem says nothing about the learnability of the weights of such a network.
These are open theoretical questions.
Given a network design, how are we going to learn weights for the neurons?
Training neural networks comprises of the following steps¶
- A forward pass, making predictions on training data.
- A loss function measures the error of the model’s predictions during that forward pass.
- Backpropagation of error, or a backward pass, to calculate the partial derivatives of the loss function.
- Gradient descent, to update model weights.
Backpropagation¶
Backpropagation is an efficient algorithm for computing the partial derivatives needed by the gradient descent update rule. For a training example $x$ and loss function $C$ in a network with $N$ layers:
- Feedforward. For each layer $l$ compute
$$a^{l} = \sigma(z^{l})$$ where $z$ is the weighted input and $a$ is the activation induced by $x$ (these are vectors representing all nodes of layer $l$).
- Compute output error
where $ \nabla_a C_j = \partial C / \partial a^N_j$, the gradient of the loss with respect to the output activations. $\odot$ is the elementwise product.
- Backpropagate the error
- Calculate gradients
Stochastic Gradient Descent¶
Randomly select $m$ training examples $X_j$ and compute the gradient of the loss function ($L$). Update weights and biases with a given learning rate $\eta$.
$$ w_k' = w_k-\frac{\eta}{m}\sum_j^m
\frac{\partial C_{X_j}}{\partial w_k}$$
$$b_l' = b_l-\frac{\eta}{m}
\sum_j^m \frac{\partial C_{X_j}}{\partial b_l}
$$
Convolution Filters¶
A filter applies a convolution kernel to an image.
The kernel is represented by an $n$x$n$ matrix where the target pixel is in the center.
The output of the filter is the sum of the products of the matrix elements with the corresponding pixels.
Examples from Wikipedia:
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| Identity | Blur | Edge Detection |
from skimage import io, img_as_float
from skimage.filters import gaussian, laplace
import matplotlib.pyplot as plt
import numpy as np
# Load the biological image (replace 'path_to_image.jpg' with your image path)
image_path = './files/bioimage.png'
original_image = img_as_float(io.imread(image_path)) # Convert image to float for processing
# Apply Gaussian blur using skimage
blurred_image = gaussian(original_image, sigma=2, channel_axis=2)
# Display the original and blurred images
plt.figure(figsize=(10, 5))
# Original Image
plt.subplot(1, 2, 1)
plt.title('Original Image')
plt.imshow(original_image)
plt.axis('off')
# Blurred Image
plt.subplot(1, 2, 2)
plt.title('Blurred Image')
plt.imshow(blurred_image)
plt.axis('off')
plt.show()
# Apply laplacian using skimage
blurred_image = laplace(original_image, ksize=3)
# Display the original and blurred images
plt.figure(figsize=(10, 5))
# Original Image
plt.subplot(1, 2, 1)
plt.title('Original Image')
plt.imshow(original_image)
plt.axis('off')
# Blurred Image
plt.subplot(1, 2, 2)
plt.title('Edge Detection')
plt.imshow(blurred_image)
plt.axis('off')
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers). Got range [-2.0549019607843135..2.4627450980392154].
Feature Maps¶
We can think of a kernel as identifying a feature in an image and the resulting image as a feature map that has high values (white) where the feature is present and low values (black) elsewhere.
Feature maps retain the spatial relationship* between features present in the original image.*
Convolutional Layers¶
A single kernel is applied across the input. For each output feature map there is a single set of weights.
Convolutional Layers¶
For images, each pixel is an input feature. Each hidden layer is a set of feature maps.
Pooling¶
Pooling layers apply a fixed convolution (usually the non-linear MAX kernel). The kernel is usually applied with a stride to reduce the size of the layer.
- faster to train
- fewer parameters to fit
- less sensitive to small changes (MAX)
The last features maps are typically connected to one or more fully-connected layers to produce the desired output.
Consider an input image with 100 pixels. In a classic neural network, we hook these pixels up to a hidden layer with 10 nodes. In a CNN, we hook these pixels up to a convolutional layer with a 3x3 kernel and 10 output feature maps.
Question: "Which network has more parameters to learn?",¶
- Classic
- CNN